Animated proof · ~14 s
a² − b² = (a + b)(a − b) — watch the cut
A big square loses a small square. The leftover L is cut once, the tall arm swings flat, and the exact same area becomes a rectangle (a + b) wide and (a − b) tall. Uses the a and b sliders above.
a = b makes the L vanish — the animation shows b just under a so there is still something to cut.